Besides shortening the life of the tire and increasing the amount of damage that you do to the lawn, I don't think I'd try this. Big spaces in tires are there for clearing out mud. Not for traction. The bigger the lugs, the harder it is for mud to stick to the tire. The smaller the lugs, the less noise a tire makes and the better it drives on the road.
Instead, try letting some air out of the tire to lower it's pressure. Lower air pressure in the tire will give you a bigger footprint, more ground contact, and more traction. Try ten pounds, if thats not enough, go down to five pounds, but be warned that you might spin the tire off the rim when you get too low.
Good luck,
Eddie